Mathematics Senior Capstone Papers


Jaron Williams

Document Type


Publication Date

Spring 2019


Originally, closed-orbit theory was developed in order to analyze oscillations in the near ionization threshold (Rydberg) densities of states for atoms in strong external electric and magnetic fields. Oscillations in the density of states were ascribed to classical orbits that began and ended near the atom. In essence, observed outgoing waves following the classical path return and interfere with original outgoing waves, giving rise to oscillations. Elastic scattering from one closed orbit to another gives additional oscillations in the cross-section. This study examines how quantum theory can be properly used in combination with classical orbit theory in order to study inelastic scattering for atoms in an external field. At Rydberg states, an electron wave function can be modeled numerically through semiclassical means, using the Coulombic interaction from the atom, but as it approaches lower states, it must be modeled quantum mechanically, using a ‘Modified Coulombic’ potential.